In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation \[ (r(t)\Phi (u^{\prime }(t)))^{\prime }+c(t)\Phi (u(t))=0, \] where (i) $r,c\in C([t_{0}, \infty )$, $\mathbb{R}:=(-\infty , \infty ))$ and $r(t)>0$ on $[t_{0},\infty )$ for some $t_{0}\ge 0$; (ii) $\Phi (u)=|u|^{p-2}u$ for some fixed number $p> 1$. We also generalize some results of Hille-Wintner, Leighton and Willet.
The purpose of this paper is to give a short conceptual description of the following three problems: actual status of the ORBITA Computer System, computation of the motion of the satellite - subsatellite system and mathematical formulation of the unmodeled accelerations in the satellite motion as coded in ORBITA system.
In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_{2n}$. We show that $B_{2n}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_{2n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.
In the paper the problem of mathematical properties of B-operations and weak WB-operations introduced by the author for interpretation of connectives "and'', "or'', and "also'' in fuzzy rules is considered. In previous author's papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if - then. Monotonicity condition, required for triangular norms, is replaced by condition of positivity (negativity), i. e. operations must be only positively (negatively) defined. Weak B-operations may not fulfill associativity condition.
By making use of the known concept of neighborhoods of analytic functions we prove several inclusions associated with the $(j,\delta )$-neighborhoods of various subclasses of starlike and convex functions of complex order $b$ which are defined by the generalized Ruscheweyh derivative operator. Further, partial sums and integral means inequalities for these function classes are studied. Relevant connections with some other recent investigations are also pointed out.